Shift-A only gives option to add Mesh?
Make sure that you are in Object Mode if you'd like to add a new primitive or new object to the scene. 

From the manual: 


  Creation of a mesh primitive typically starts by adding a mesh object
  in Object Mode. Limited types of editing such as size, location, and
  orientation can be accomplished in Object Mode. Object Mode also
  provides the means to Join and Group multiple mesh primitives.